On the Laplacian-Energy-Like Invariant of Graphs

Abstract

The Laplacian-energy-like graph invariant of a graph $G$, denoted by $LEL(G)$, is defined as $LEL(G)=\sum _{i=1}^n\sqrt{{\mu }_i}$, where ${\mu }_i$ are the Laplacian eigenvalues of graph $G$. In this paper, we study the maximum $LEL$ among graphs with a given number of vertices and matching number. Some results on $LEL(G)$ and $LEL(\overline{G})$ are obtained.